# ${L}^{p}$-${L}^{q}$-Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity

Annales Polonici Mathematici (1991)

- Volume: 54, Issue: 2, page 135-145
- ISSN: 0066-2216

## Access Full Article

top## Abstract

top## How to cite

topJerzy Gawinecki. "$L^p$-$L^q$-Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity." Annales Polonici Mathematici 54.2 (1991): 135-145. <http://eudml.org/doc/262394>.

@article{JerzyGawinecki1991,

abstract = {We prove the $L^p$-$L^q$-time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman’s approach [12], [5] to the $L^p$-$L^q$-time decay estimates.},

author = {Jerzy Gawinecki},

journal = {Annales Polonici Mathematici},

keywords = {decay estimates; partial differential equations; Cauchy problem; symmetric hyperbolic system of first order; linear thermoelasticity; global existence in time},

language = {eng},

number = {2},

pages = {135-145},

title = {$L^p$-$L^q$-Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity},

url = {http://eudml.org/doc/262394},

volume = {54},

year = {1991},

}

TY - JOUR

AU - Jerzy Gawinecki

TI - $L^p$-$L^q$-Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity

JO - Annales Polonici Mathematici

PY - 1991

VL - 54

IS - 2

SP - 135

EP - 145

AB - We prove the $L^p$-$L^q$-time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman’s approach [12], [5] to the $L^p$-$L^q$-time decay estimates.

LA - eng

KW - decay estimates; partial differential equations; Cauchy problem; symmetric hyperbolic system of first order; linear thermoelasticity; global existence in time

UR - http://eudml.org/doc/262394

ER -

## References

top- [1] R. Adams, Sobolev Spaces, Academic Press, New York 1975.
- [2] K. O. Friedrichs, Symmetric hyperbolic linear differential equations, Comm. Pure Appl. Math. 7 (1954), 345-392. Zbl0059.08902
- [3] Yu. V. Egorov, Linear Differential Equations of Principal Type, Nauka, Moscow 1984 (in Russian).
- [4] J. Gawinecki, Matrix of fundamental solutions for the system of equations of hyperbolic thermoelasticity with two relaxation times and solution of the Cauchy problem, Bull. Acad. Polon. Sci., Sér. Sci. Techn. 1988 (in print). Zbl0698.73003
- [5] S. Klainerman, Global existence for nonlinear wave equations, Comm. Pure Appl. Math. 33 (1980), 43-101. Zbl0405.35056
- [6] S. Klainerman, Long-time behaviour of solutions to nonlinear evolution equations, Arch. Rational Mech. Anal. 78 (1982), 72-98. Zbl0502.35015
- [7] S. Klainerman and G. Ponce, Global, small amplitude solutions to nonlinear evolution equations, Comm. Pure Appl. Math. 36 (1983), 133-141. Zbl0509.35009
- [8] J. L. Lions et E. Magenes, Problèmes aux limites non homogènes et applications, Dunod, Paris 1968. Zbl0165.10801
- [9] A. Piskorek, Fourier and Laplace transformation with their applications, Warsaw University, 1988 (in Polish).
- [10] J. Shatah, Global existence of small solutions to nonlinear evolution equations, J. Differential Equations 46 (1982), 409-425. Zbl0518.35046
- [11] S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics, 3th ed. Nauka, Moscow 1988 (in Russian). Zbl0662.46001
- [12] W. A. Strauss, Nonlinear scattering theory at low energy, J. Funct. Anal. 41 (1981), 110-113. Zbl0466.47006
- [13] E. S. Suhubi, Thermoelastic solids, in: Continuum Physics, A. C. Eringen (ed.), Academic Press, New York 1975.
- [14] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, Deutscher Verlag der Wissenschaften, Berlin 1978. Zbl0387.46033